Three-dimensional localized Airy elegant Laguerre–Gaussian light bullets in free space

By solving the ( 3 + 1)-dimensional ((3 + 1)D) free-space Schrodinger equation of an optical field analytically, we have demonstrated 3D controllable Airy elegant Laguerre-Gaussian (AiELG) wave packets, even mode AiELG wave packets, and odd mode AiELG wave packets in free space. AiELG wave packets are constructed by Airy pulses with an initial velocity in the temporal domain and the elegant Laguerre-Gaussian (elegant LG) beams in the space domain. Furthermore, we demonstrate the numerical experiments of the elegant LG beams to study their evolution properties. Finally, we draw a conclusion that the evolution properties of the light bullets are influenced by the initial velocity, evolution distance, and mode numbers.